-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3477053642938866095620168991683', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [5.196152422706632, 0.0], 'a4': [0.0, -8.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [5.588457268119896, 5.588457268119896], 'a8': [0.0, 0.0], 'a9': [27.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.301074490223885, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-5.196152422706632, 0]]], [13, [[1.0, 0], [31.176914536239792, -35.0]]]], 'bad_primes': [3, 13], 'central_character': '39.5', 'coefficient_field': 'CDF', 'conductor': 39, 'conductor_radical': 39, 'conjugate': '2605039357992325058764600090073', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0, 8.0]], [[1.0, 0], [-5.196152422706632, 0]], [[1.0, 0], [0, 0], [0, 125.0]], [[1.0, 0], [-5.588457268119896, -5.588457268119896], [0, 343.0]], [[1.0, 0], [0, 0], [0, -1331.0]], [[1.0, 0], [31.176914536239792, -35.0]], [[1.0, 0], [0, 0], [4913.0, 0]], [[1.0, 0], [105.94228634059948, -105.94228634059948], [0, -6859.0]], [[1.0, 0], [0, 0], [12167.0, 0]], [[1.0, 0], [0, 0], [-24389.0, 0]], [[1.0, 0], [-76.05771365940052, 76.05771365940052], [0, -29791.0]], [[1.0, 0], [-273.23840175367854, -273.23840175367854], [0, 50653.0]], [[1.0, 0], [0, 0], [0, 68921.0]], [[1.0, 0], [0, 218.23840175367854], [-79507.0, 0]], [[1.0, 0], [0, 0], [0, -103823.0]], [[1.0, 0], [0, 0], [-148877.0, 0]], [[1.0, 0], [0, 0], [0, -205379.0]], [[1.0, 0], [935.3074360871938, 0], [226981.0, 0]], [[1.0, 0], [-767.3576026305178, 767.3576026305178], [0, -300763.0]], [[1.0, 0], [0, 0], [0, 357911.0]], [[1.0, 0], [782.0614872174388, 782.0614872174388], [0, 389017.0]], [[1.0, 0], [-1091.1920087683927, 0], [493039.0, 0]], [[1.0, 0], [0, 0], [0, 571787.0]], [[1.0, 0], [0, 0], [0, -704969.0]], [[1.0, 0], [1350.8921197972754, -1350.8921197972754], [0, -912673.0]], [[1.0, 0], [0, 0], [1030301.0, 0]], [[1.0, 0], [0, 1028.8381796959131], [-1092727.0, 0]], [[1.0, 0], [0, 0], [-1225043.0, 0]], [[1.0, 0], [768.1920087683927, -768.1920087683927], [0, -1295029.0]], [[1.0, 0], [0, 0], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-39-39.5-c3-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/39/4/f/a/5/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6754642864850264, 1.7047398352234702, 1.731229353947566, 1.7546528659958165, 1.7743727112623224, 1.789412072658545, 1.7984868274584924, 1.8000499492977375, 1.792347760690678, 1.7734875107687362, 1.7415158993317323, 1.6945081688789894, 1.6306671633217826, 1.548431276372201, 1.4465894983376668, 1.3244008635237852, 1.181714568894559, 1.019085958071394, 0.8378825310601545, 0.6403732422204466, 0.4297936827075994, 0.21037940474355157, -0.012640274572671787, -0.23309507032014434, -0.44397905874779564, -0.6376127107544963, -0.8058634253195136, -0.9404233934387594, -1.0331401478830602, -1.0763912972479583, -1.063490885823005, -0.9891107958424841, -0.8496968916435953, -0.643856504442655, -0.3726916959389624, -0.04005183744715702, 0.34732031314364403, 0.7797724318408471, 1.2448753997576512, 1.7277177887460298, 2.2113666976969037, 2.677489875296426, 3.1071232189103553, 3.481556333181313, 3.7832975919980885, 3.997069907624354, 4.11078006517702, 4.116398923022353, 4.010687831710978, 3.795708957647418, 3.479064256169736, 3.0738197643735528, 2.5980884587188084, 2.0742655292288386, 1.527933534457062, 0.9864801061367463, 0.4774959292285958, 0.0270436617992764, -0.34209278791958, -0.6120566472448277, -0.771337736631314, -0.8158410834186407, -0.7494974701719405, -0.5843333956130327, -0.3399517718491849, -0.042415931546672246, 0.27742441400887985, 0.5860790524903957, 0.8499035276740481, 1.0377554884148157, 1.1236224113075932, 1.0890074774992111, 0.9248625004184403, 0.6328770391223606, 0.22597123344243122, -0.2721051310153488, -0.8280965444840853, -1.4014411420279376, -1.9472188440616753, -2.4196470132731545, -2.775859558913098, -2.979661188039633, -3.0049285839787214, -2.8383386597937, -2.481142342785439, -1.9497695316758852, -1.2751429846544762, -0.5006892212393246, 0.32084604519968557, 1.1315526769224193, 1.8731513087332643, 2.492019162676451, 2.9439908329002367, 3.19847384178739, 3.241458992681105, 3.0770897536329076, 2.7275777399998056, 2.2314030592647174, 1.639905329584625, 1.0125374436247085, 0.41120235028498564, -0.10579337535446151, -0.48957078414332234, -0.7056904701814671, -0.7377984377180202, -0.5894776754879983, -0.28404773108951514, 0.13773811549252474, 0.6219247828174814, 1.1071266086482696, 1.531263046792229, 1.8385529606393554, 1.9860022987668347, 1.9486431519315792, 1.7228900566545726, 1.327564464229146, 0.8023837096768227, 0.20399172898701784, -0.4001053452553254, -0.9390777073930826, -1.3469653362692653, -1.5705952351864296, -1.5762834153727967, -1.3544852698430156, -0.9217648557419464, -0.319745349563399, 0.38895113022745625, 1.1274050477638202, 1.813039854699048, 2.3672355821421194, 2.724792399264136, 2.842093705996404, 2.7029311791164825, 2.3211998966162644, 1.7400259831440166, 1.0273129736958608, 0.26813631213358075, -0.4451769019081264, -1.0241268566226507, -1.3949369167314976, -1.5079018621066262, -1.3439738548552311, -0.9176823795817628, -0.27592272713574195, 0.5073382703524743, 1.339864565517147, 2.1224172011933167, 2.7610916994096937, 3.1791561850390155, 3.326843905241087, 3.187783643255141, 2.7811639967724386, 2.1592737006834595, 1.4006710017610011, 0.5998297453616307, -0.14539355517417563, -0.7468004827490103, -1.1376219366124813, -1.2813792934467558, -1.1765641594316791, -0.8564230319360296, -0.3838072583676735, 0.1582522630515733, 0.6789606822582123, 1.0934200286698317, 1.3355672074222216, 1.368475541967936, 1.1904399325049728, 0.8358399583958986, 0.37051486730501576, -0.1178129468008426, -0.5327792078172384, -0.7844116283819809, -0.803756036858421, -0.5548812193500265, -0.04236412687664993, 0.6870343257562577, 1.5489707931718493, 2.431946232010862, 3.2122215841081108, 3.7711717664237647, 4.012595834779046, 3.8774272325129595, 3.353594838086052, 2.479439386983618, 1.340003109224207, 0.05655287551697308, -1.2292855896718275, -2.374568433683581, -3.2545126649292575, -3.7795566257286657, -3.9074570133252524, -3.648584615611389, -3.063584024425368, -2.253713326037631, -1.3453024303829242, -0.47068706889656875, 0.2514592505607427, 0.7333577761562972, 0.9302465623217434, 0.8455097478346463, 0.5280365227512227, 0.06227768798629343, -0.4473447434282736, -0.8950841317939947, -1.192456319077703, -1.2836322067273056, -1.1550012461779269, -0.8372205271342109, -0.39931462801332007, 0.06425861485393952, 0.45143576314085504, 0.672236733196021, 0.6668849815115021, 0.4191054643548041, -0.03791546323948255, -0.6242343379563162, -1.2243923145006332, -1.705590963878863, -1.9399493757849027, -1.827187669281491, -1.3138778410872274, -0.40584996648149185, 0.8286161926610417, 2.2657068921679335, 3.742316810859643, 5.079247901308817, 6.107762081416254, 6.6952301924971485, 6.765669035625272, 6.311721231950051, 5.395995578615073, 4.14142845490301, 2.7121585093294045, 1.2880138781410013, 0.03681199026290924, -0.9109329415650663, -1.4806908064432578, -1.6629025725995639, -1.5108579177886494, -1.1279750341860781, -0.6468446955748833, -0.20384574054670507, 0.08608398318808318, 0.14997607388755957, -0.031027560549801915, -0.42007555549410974, -0.9337657508714563, -1.4602828420447662, -1.8830496125309057, -2.1053636700162186, -2.071259732880227, -1.7784939633749597, -1.2809856636301156, -0.6800191619933115, -0.10564708034811456, 0.30835251990487267], 'positive_zeros': ['2.74291168427077067100408965529681', '4.38873976500028456531636509264426', '7.13323445016229607942645609588615', '8.141802739025896144043196910425122', '9.309102329239299315269604686838755', '10.95147971079917507375939622503676', '12.59699299404818048346881928192143', '13.33693457882400599878000709476108', '14.66661610876046431219491568700498', '15.68295580031772008889168602981897'], 'prelabel': '2-39-39.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5169292963826246, 'root_angle': 0.13804791656140034, 'root_number': '0.907421176940968 + 0.4202223311998881*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0690239582807', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.74291168427077067100408965530', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.38873976500028456531636509264', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.13323445016229607942645609589', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.301074490223885, 'bad_primes': [3, 13], 'central_character': '39.5', 'conductor': 39, 'conductor_radical': 39, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/39/4/f/a/5/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-39-39.5-c3-0-6', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-39-39.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5169292963826246, 'root_angle': 0.06902395828070017, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.74291168427077067100408965530', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3477053642938866095620168991683', 'Lhash_array': ['3477053642938866095620168991683'], 'label': '2-39-39.5-c3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/39/4/f/a/5/2'}